2020
DOI: 10.48550/arxiv.2007.16132
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Bell polynomials in the series expansions of the Ising model

Grzegorz Siudem,
Agata Fronczak

Abstract: Through applying Bell polynomials to the integral representation of the free energy of the Ising model for the triangular and hexagonal lattices we obtain the exact combinatorial formulas for the number of spin configurations at a given energy (i.e. low-temperature series expansion of the partition function or, alternatively, the number of states). We also generalize this approach to the wider class of the (chequered) Utiyama graphs. Apart from the presented exact formulas, our technique allows one to establis… Show more

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